Mathematics has been called the language of the universe. Scientists and engineers often speak of the elegance of mathematics when describing physical reality, citing examples such as π, E=mc2, and even something as simple as using abstract integers to count real-world objects. Yet while these examples demonstrate how useful math can be for us, does it mean that the physical world naturally follows the rules of mathematics as its "mother tongue," and that this mathematics has its own existence that is out there waiting to be discovered? This point of view on the nature of the relationship between mathematics and the physical world is called Platonism, but not everyone agrees with it.

Derek Abbott, Professor of Electrical and Electronics Engineering at The University of Adelaide in Australia, has written a perspective piece to be published in the Proceedings of the IEEE in which he argues that mathematical Platonism is an inaccurate view of reality. Instead, he argues for the opposing viewpoint, the non-Platonist notion that mathematics is a product of the human imagination that we tailor to describe reality.

This argument is not new. In fact, Abbott estimates (through his own experiences, in an admittedly non-scientific survey) that while 80% of mathematicians lean toward a Platonist view, engineers by and large are non-Platonist. Physicists tend to be "closeted non-Platonists," he says, meaning they often appear Platonist in public. But when pressed in private, he says he can "often extract a non-Platonist confession."

So if mathematicians, engineers, and physicists can all manage to perform their work despite differences in opinion on this philosophical subject, why does the true nature of mathematics in its relation to the physical world really matter?

The reason, Abbott says, is that because when you recognize that math is just a mental construct—just an approximation of reality that has its frailties and limitations and that will break down at some point because perfect mathematical forms do not exist in the physical universe—then you can see how ineffective math is.

And that is Abbott's main point (and most controversial one): that mathematics is not exceptionally good at describing reality, and definitely not the "miracle" that some scientists have marveled at. Einstein, a mathematical non-Platonist, was one scientist who marveled at the power of mathematics. He asked, "How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?"

In 1959, the physicist and mathematician Eugene Wigner described this problem as "the unreasonable effectiveness of mathematics." In response, Abbott's paper is called "The Reasonable Ineffectiveness of Mathematics." Both viewpoints are based on the non-Platonist idea that math is a human invention. But whereas Wigner and Einstein might be considered mathematical optimists who noticed all the ways that mathematics closely describes reality, Abbott pessimistically points out that these mathematical models almost always fall short.

"Analytical mathematical expressions are a way making compact descriptions of our observations," he told Phys.org. "As humans, we search for this 'compression' that math gives us because we have limited brain power. Maths is effective when it delivers simple, compact expressions that we can apply with regularity to many situations. It is ineffective when it fails to deliver that elegant compactness. It is that compactness that makes it useful/practical ... if we can get that compression without sacrificing too much precision.

"I argue that there are many more cases where math is ineffective (non-compact) than when it is effective (compact). Math only has the illusion of being effective when we focus on the successful examples. But our successful examples perhaps only apply to a tiny portion of all the possible questions we could ask about the universe."

Some of the arguments in Abbott's paper are based on the ideas of the mathematician Richard W. Hamming, who in 1980 identified four reasons why mathematics should not be as effective as it seems. Although Hamming resigned himself to the idea that mathematics is unreasonably effective, Abbott shows that Hamming's reasons actually support non-Platonism given a reduced level of mathematical effectiveness.

Here are a few of Abbott's reasons for why mathematics is reasonably ineffective, which are largely based on the non-Platonist viewpoint that math is a human invention:

• Mathematics appears to be successful because we cherry-pick the problems for which we have found a way to apply mathematics. There have likely been millions of failed mathematical models, but nobody pays attention to them. ("A genius," Abbott writes, "is merely one who has a great idea, but has the common sense to keep quiet about his other thousand insane thoughts.")

• Our application of mathematics changes at different scales. For example, in the 1970s when transistor lengths were on the order of micrometers, engineers could describe transistor behavior using elegant equations. Today's submicrometer transistors involve complicated effects that the earlier models neglected, so engineers have turned to computer simulation software to model smaller transistors. A more effective formula would describe transistors at all scales, but such a compact formula does not exist.

• Although our models appear to apply to all timescales, we perhaps create descriptions biased by the length of our human lifespans. For example, we see the Sun as an energy source for our planet, but if the human lifespan were as long as the universe, perhaps the Sun would appear to be a short-lived fluctuation that rapidly brings our planet into thermal equilibrium with itself as it "blasts" into a red giant. From this perspective, the Earth is not extracting useful net energy from the Sun.

• Even counting has its limits. When counting bananas, for example, at some point the number of bananas will be so large that the gravitational pull of all the bananas draws them into a black hole. At some point, we can no longer rely on numbers to count.

• And what about the concept of integers in the first place? That is, where does one banana end and the next begin? While we think we know visually, we do not have a formal mathematical definition. To take this to its logical extreme, if humans were not solid but gaseous and lived in the clouds, counting discrete objects would not be so obvious. Thus axioms based on the notion of simple counting are not innate to our universe, but are a human construct. There is then no guarantee that the mathematical descriptions we create will be universally applicable.

For Abbott, these points and many others that he makes in his paper show that mathematics is not a miraculous discovery that fits reality with incomprehensible regularity. In the end, mathematics is a human invention that is useful, limited, and works about as well as expected.

For those who seek something more practical out of such a discussion, Abbott explains that this understanding can allow for greater freedom of thought. One example is an improvement of vector operations. The current method involves dot and cross products, "a rather clunky" tool that does not generalize to higher dimensions. Lately there has been a renewed interest in an alternative approach called geometric algebra, which overcomes many of the limitations of dot and cross products and can be extended to higher dimensions. Abbott is currently working on a tutorial paper on geometric algebra for electrical engineers to be published in the near future.

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206 comments

"In retrospect, it seems clear that Alfvén considered his early theoretical assumption of frozen-in magnetic fields to be his greatest mistake, a mistake perpetuated first and foremost by mathematicians attracted to Alfvén's magnetohydrodynamic equations. Alfvén came to recognize that real plasma behavior is too "complicated and awkward" for the tastes of mathematicians. It is a subject "not at all suited for mathematically elegant theories." It requires hands-on attention to plasma dynamics in the laboratory. Sadly, he said, the plasma universe became "the playground of theoreticians who have never seen a plasma in a laboratory. Many of them still believe in formulae which we know from laboratory experiments to be wrong.""

, why does the true nature of mathematics in its relation to the physical world really matter?

while I agree with him that maths is something we conjured up this question seems to go past the point:We make the math to fit the application (before anyone misconstrues this: no, we do not make the SOLUTION to fit the problem - we merely invent the tools that we think are helpful for a certain set of problems and then try out whether they are actually useful.)

So while a current set of matehematical methods may not be effective at solving an issue another set of matehmatics may well be. The author makes it out as if mathematics were something static. Far from it.

The real central point of using math, however is this idea:We perceive (and believe) the universe to be self consistent. Math is also self consistent. So we try to map the one onto the other.

This seems to be an unreasonable criticism. That math maps onto the universe does not mean that all the universe has to map onto math (i.e. that for every possible expression of a mathematical/physical theorem there has to be a corresponding reality...that would be Platonism)

but such a compact formula does not exist.

It does exist. It's just too hard to compute (simulation is way faster). The author's distinction of what makes a simple/elegant formula and what doesn't seems rather arbitrary. That a formula is bigger than one can keep in mind does not make it less elegant than a shorter one.

Even counting has its limits. When counting bananas, for example, at some point the number of bananas will be so large that the gravitational pull of all the bananas draws them into a black hole. At some point, we can no longer rely on numbers to count

"Again and again Alfvén reiterated the point: the underlying assumptions of cosmologists today "are developed with the most sophisticated mathematical methods and it is only the plasma itself which does not 'understand' how beautiful the theories are and absolutely refuses to obey them.""

---

That said, I do still wonder if cosmologists/astrophysicists were to include the observed behavior of laboratory plasmas in their inferences for cosmic plasmas, perhaps machine learning algorithms could nevertheless sort out much of the confusion. We're still at a point in cosmology where most infer velocities for radio redshifts centered near critical ionization velocities without much thought put into the inherent politics of such inferences -- even when those inferred velocities are anomalous.

If each time an inference is made, the tool of mathematics is only used to support the existing theory, then the tool of mathematics becomes subordinate to our own pre-existing expectations.

Thus axioms based on the notion of simple counting are not innate to our universe, but are a human construct.

Ah. Captain Obvious strikes.

However we still don't know whether the universe is, at its core, quantized. So I wouldn't count out the possibility of countability just yet.

But that there is no natural boundary that distinguishes THIS from THAT is rather trivial. It is one of the aspects of using SOME math based models. There are plenty of math based models that don't use integers. For a lot of issues that are useful to us integer based models are good enough.

mathematics is not a miraculous discovery that fits reality with incomprehensible regularity.

It's like the puddle (math) and the pond (the universe). You develop the math that fits the universe. The longer you fiddle with it the better it fits.

Some more thought that just came to me is that based on Jacob Bronowski's findings, mathematics starts from our current perspectives. It is also about overcoming our current perspective limitations. I actually don't get into this part of Jacob Bronowski's "Origins of Knowledge and Imagination" in my article linking some remarkable connections in James Burke's "Connections" and Jacob Bronowski's ideas in his "Origins" book already mentioned. Jacob gets much more into the biology in the book.

The core of reality is structure. Structure is deeper than particles, fields and energy. Even the quantum vacuum has structure, which is necessary to release particles and energy from 'nothing.' Nothing itself still has structure. So as maths mimic structure they mimic the most ephemeral element of reality itself, which is often beyond the reach of perception

Re: "Mathematics appears to be successful because we cherry-pick the problems for which we have found a way to apply mathematics. There have likely been millions of failed mathematical models, but nobody pays attention to them."

This might be the most important claim in the article. Part of the problem of our university system (and even websites/forums like this one) is that there is no ongoing effort to systematically catalog all of this claimed cherry-picking. Each time that a problem is raised, the models are simply made more complex, and those who point to competing ideas which might better explain the observation are ostracized/ridiculed.

In any other endeavor, this would be considered defensive behavior. When "thinking like a scientist" is no longer simply a set of human virtues and methodologies, but also includes ideologies, then assumptions go unquestioned, and mathematics becomes a weapon which is used to both confirm that ideology and destroy competitors.

This might be the most important claim in the article. Part of the problem of our university system (and even websites/forums like this one) is that there is no ongoing effort to systematically catalog all of this claimed cherry-picking. Each time that a problem is raised, the models are simply made more complex, and those who point to competing ideas which might better explain the observation are ostracized/ridiculed.

In any other endeavor, this would be considered defensive behavior. When "thinking like a scientist" is no longer simply a set of human virtues and methodologies, but also includes ideologies, then assumptions go unquestioned, and mathematics becomes a weapon which is used to both confirm that ideology and destroy competitors.

says the guy that KNOWS plasma cosmology to be true, and the "proof" is that it's so obnoxious, serious thinkers ignore it...proving that "mainstream science" is a false dichotomy since they won't take your obnoxiousness seriously...

Even counting has its limits. When counting bananas, for example, at some point the number of bananas will be so large that the gravitational pull of all the bananas draws them into a black hole. At some point, we can no longer rely on numbers to count.

I laughed because it's just not true. A given volume of bananas would not condense into a black hole. The math is basically this:

A 1.4 solar mass black hole (2.8x10^30 kg) has a diameter of 30km (14 trillion cubic meters). These are the vital statistics for the smallest black hole, give or take, that you can make just by letting stuff fall in on itself.

A banana weighs 0.125kg and has a density of 0.2 (much less than water). It takes 11.2 x10^30 bananas to equal 1.4 solar masses. That's 7x10^30 cubic liters. And that volume of bananas fills a sphere roughly 23.8 million kilometers in diameter.

"Mathematics appears to be successful because we cherry-pick the problems for which we have found a way to apply mathematics."

You get this type of straw man arguments when you have engineers mess with philosophy of science. The aim of physics is a ToE via the use of mathematics. The only missing part is quantum gravity and a ToE is possible. This means that every conceivable phenomenon will be described by these ToE. This is not an issue of Platonists versus constructivists. This is a strawman argument. The issue is whether gravity can be quantized. All else is senseless argumentation. If gravity is an "outside force" then our math will never describe this reality because it is a computer simulation http://t.co/jwS8lxlc

I completely disagree that math is inappropriate to describe reality simply because it isn't complete.

I would like to point to my previous sentence as evidence to support itself. No, I'm not kidding. If my sentence was effective, then it would describe everything perfectly.

If you agree with him, then there is no such thing as a colloseum. His example says that one math should describe all situations. If so, then one single colloseum should seat all people for all events, and everyone should have a good seat. Oh, and since The Colloseum in Rome isn't all there, then it's totally useless; bulldoze it down.

Geometry and numerical relationships are there whether people discover and name them or not. It's human interpretation of math that is lacking or incomplete, not the natural numerical relationships that exist with or without us.

Geometric proofs, chords, harmonics, discrete objects, etc. all exist whether there are people to name them and use them or not. This guy is a loone.

The cricitism boils down to the simple realization that the map is not the territory.

In other words, while math can provide a perfect representation of reality like you can draw a perfect map, the perfect map would be a 1:1 replica of the territory, and as such would be perfectly useless.

When counting bananas, for example, at some point the number of bananas will be so large that the gravitational pull of all the bananas draws them into a black hole. At some point, we can no longer rely on numbers to count.

Damn, they plagiarized my banana theory,... which was to compete with AWT.

What an absurd article. Arguing that math isn't the root of the universe is equivalent to saying that the universe doesn't behave according to logical rules. And it isn't possible, even as a concept, to have a universe that doesn't run on logical rules. It's simply a nonsensical statement.

Oh, and I'm a physicist. I'd love to meet some of these so-called "closeted non-Platonist" physicists, but I suspect they're actually few and far between, and that Dr. Abbott is mostly inventing his crowd of supporters.

What an absurd article. Arguing that math isn't the root of the universe is equivalent to saying that the universe doesn't behave according to logical rules. And it isn't possible, even as a concept, to have a universe that doesn't run on logical rules. It's simply a nonsensical statement.

Oh, and I'm a physicist. I'd love to meet some of these so-called "closeted non-Platonist" physicists, but I suspect they're actually few and far between, and that Dr. Abbott is mostly inventing his crowd of supporters.

oh, they exist. but the further away models get from daily life, the harder it is from some to appreciate. everyone gets 2+2, because you can count out 4 apples, but you cannot count Ď� apples, let alone imaginary #'s like i. are models *perfect* for explaining nature? usually not. doesn't make them "wrong". same thing here, i'd suggest.

in other words, verbal wanking semantics. and i basically just plagiarized Cryptonomicon :)

while 80% of mathematicians lean toward a Platonist view, engineers by and large are non-Platonist

Well obviously this is because they are not as good at math as mathematicians.

Physicists tend to be "closeted non-Platonists," he says, meaning they often appear Platonist in public. But when pressed in private, he says he can "often extract a non-Platonist confession."

I think this is an expression of how religious dogma has so thoroughly poisoned society, along with its evil younger brother, metaphysics.

Physicists cant just sit and do math all day, they have to experiment with complex and expensive machinery built by, well, engineers. It can be frustrating and we can understand if physicists will become irrational some times and start writing poetry or something.

Math never failed to describe something where words only made it worse.

"As far of the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."- Albert Einstein

I think what Einstein was referring to was the analytic / synthetic distinction. An analytic proposition is one that is logically certain, but in which we can not learn anything new (the predicate in contained in the subject),.... while a synthetic proposition is one that is not certain, but one for which we can learn new things.

Analytic propositions are a-priori (knowledge prior to and independent of experience) and are dependent upon our definitions (axioms). Synthetic propositions are a-postori and are contingent upon a conjunction of empirical observations.

How is it possible then that mathematics works so well in describing reality? What's the connection between the analytic and synthetic distinction? .....

We must have evolved a-priori synthetic intuitions,... intellectual faculties that determine the form of experience, and so the conditions for the understanding. For example, space and time are a-priori intuitions necessary for a synthesis of experience to be possible. It is a means the mind has evolved to order experience. Our choice of logical axioms may likewise be guided automatically in our intuitions.

That the mind evolved to operate on empirical reality is unique in that reality informs the mind of what faculties will be necessary to do so,.... so they are 'guaranteed' to work.

The reason, Abbott says, is that because when you recognize that math is just a mental construct—just an approximation of reality that has its frailties and limitations and that will break down at some point because perfect mathematical forms do not exist in the physical universe—then you can see how ineffective math is.

Wow, I don't know where to begin with this absurdity.

Math is a sub-set of Logic. You don't discard a sub-set of knowledge just because it either doesn't apply to a specific situation, or just because you don't understand it.

Points 1, 2, and 3 near the end of the article are all arguments from absurdity.

In the case of a "cloud" i.e. distributed organism, the numbers are still "real" whether or not you have the ability or patience to actually count them, just as the number of people in a crowd at a rally or protest is real, whether or not you have the intelligence, tools, time or care to count them properly.

If you want to model mixing say Nitrogen gas and Oxygen gas in a air-tight box, it is evident that there actually is a discreet number of atoms, and a discreet number of molecules in the box, regardless of whether you have the time, tools, or will to count them all.

Just because a problem is difficult, or even impossible for man to solve through mathematics, does not mean that the underlying math of the situation is a fabrication of man's will.

Ignorance doesn't disprove the validity of math as an actual law of the universe and logic.

Let's take biochemistry for an example.

At some point in the distant past, people didn't know what atoms and molecules were. They just knew sugar was sweet.

Then they later learned sugar was a molecule made of atoms.

Then they later learned it's actual structure and could count the atoms and the arrangement.

The last statement was always true and always involved math, even before humans discovered it. Math isn't a fabrication of man. That's absurd.

Physicists tend to be "closeted non-Platonists," he says, meaning they often appear Platonist in public. But when pressed in private, he says he can "often extract a non-Platonist confession."

I think this is an expression of how religious dogma has so thoroughly poisoned society, along with its evil younger brother, metaphysics.

Physicists cant just sit and do math all day, they have to experiment with complex and expensive machinery built by, well, engineers. It can be frustrating and we can understand if physicists will become irrational some times and start writing poetry or something. - GhostofOtto1923

Dear dear GhostofOtto1923, you know not even what you profess to hate.

The Platonist view of mathematics IS a metaphysical one,... that there are abstract mathematical objects whose existence is independent of us and our language,.. existing "out there" independent of imperfect things of experience.

...it is evident that there actually is a discreet number of atoms, and a discreet number of molecules in the box, regardless of whether you have the time, tools, or will to count them all.

Just because a problem is difficult, or even impossible for man to solve through mathematics, does not mean that the underlying math of the situation is a fabrication of man's will.

The Fermi-Dirac statistics and the Einstein-Bose statistics were formulated precisely because of the inability of enumerating indistinguishable particles, even in principal, while their wavefunctions overlap.

Dear dear GhostofOtto1923, you know not even what you profess to hate.

The Platonist view of mathematics IS a metaphysical one,... that there are abstract mathematical objects whose existence is independent of us and our language,.. existing "out there" independent of imperfect things of experience.

But the fact that we use so-called "abstracts" every day proves that they in fact exist.

A rule which limits the scope of a logical operation or of an entire branch of knowledge does not invalidate that operation or branch of knowledge.

For example, division by zero being "undefined" doesn't make division useless. It just means division only applies to other instances. It may be that division by zero does not exist at all in reality, or it may be that it does exist and we just haven't discovered it. After all, "Imaginary numbers" were actually proposed before a physical use for them was discovered, but they are now used in describing Neutrinos.

Now the example in the above post does not undermine my argument, it just so happens to be a case where mathematical theory was ahead of the physical reality to which that math was conjoined, which is to say it's a rare case of man discovering a mathematical relationship "on paper" before it was actually discovered in reality.

Yet even that is not a fabrication, if anything it actually proves that mathematics is somehow fundamental to the universe itself, because the same mathematical operation was found in nature after it was hypothesized in pure mathematics. It wasn't a matter of discovering something in nature and then proposing a model. It was a matter of extrapolating mathematics people already understood into a realm not previously understood, and then that relationship was discovered in reality anyway.

The point here is that math can predict the universe, within the limits of our understanding, because the universe is mathematical.

@Lurker2358, my point was not to refute or accept the Platonist view in that response, but only to inform TheGhostOfOtto1923 that Platonism is a metaphysical notion.

Now, my posts priori to that WAS designed to refute Platonism (metaphysics) in placing mathematical truth and its applicability to reality in the 'hardwiring' of the mind, informed by physical reality in its evolution.

If you actually believe that mathematics is a fabrication of man, then you would need to discard all of physics and the "Standard Model" and all knowledge or alleged knowledge of atoms and sub-atomic particles, etc, because they are all based on math and numbers being real, fundamental properties of the universe.

A water molecule exists because hydrogen "wants" to form one bond, and Oxygen "wants" to form two bonds, therefore two hydrogen and one Oxygen combine to make a new molecule. the math is real, else the molecule would not exist, and even if it could somehow exist without math, we would have no way to describe it.

Once you try to claim math is a fabrication of man, then you'd have to discard it just like Unicorns and Leprechauns, and resort to what? Topology only? Well the reason math exists is because Topology cannot describe reality. Math is required. Even topology actually requires math because you can have more than one object, and more than one hole in a single object.

A water molecule exists because hydrogen "wants" to form one bond, and Oxygen "wants" to form two bonds, therefore two hydrogen and one Oxygen combine to make a new molecule.

But those molecules don't exist on the basis of knowing that. The molecules are not asking that question,... how many covalent bonds. They just are. Man comes along and constructs a model, and in so doing asks about bonds and relations between observable things, and only then do those relations have meaning. Relations between things are not themselves physical entities, but rather only questions.

I'm not exactly saying that 'math is a fabrication of man'. I'm saying that the axioms of math are informed by our a-priori intuitions, which were in turn informed by reality during the evolution of the mind,..... probably.

The logical positivist mathematicians say that mathematical axioms are dependent upon our definitions and language.

Information theory suggests that math is a real thing, and is the universal language.

The author, i.e. Abott, not Lisa Zyga, claims that computer models are used when mathematics can't describe something. Yet computers function on pure mathematics, so you can't claim a computer model is producing something which is not mathematical. In fact, everything a computer does is ultimately mathematical.

Now you are saying math is an emergent property, which is silly. You are made of water molecules, among a lot of other molecules, and all of them are based on mathematics.

Human consciousness is based on mathematics, even in the case of humans who are ignorant of math, because the molecules of the brain and body are based on mathematics.

Self awareness is not a fundamental property of mathematics, but rather an emergent property.

Forgive me if someone already spoke to this and I'm no mathematician but I read somewhere that Clerk's beautiful equations not only brought much of what was known together (electromagnetic spectrum et al) but mapped much of what had yet to be even discovered. This strikes me as relevant somehow and a far cry from "cherry-picking" what fits.

If we ever encounter an alien species, we will discover that none of our inventions are the same as their inventions. Our languages will be very different. The way we write language will be very different. Our houses, transportation machines, engines, attire, everything invented or created by us will be wildly different between us and the alien.

However, we will have huge swaths of mathematics in common. Certainly the alien species will have a total match for "integer", though they are likely not to use base 10 as their default base. I bet, however, that they will have a "base x" system as part of their mathematical model. They will have decimals, fractions, even a direct calculus equivalent. They will have the same numeric sequence (base factored in) for pi, and e. They will most likely recognize that e^(pi*i)=-1.

If the alien would have the same math as we have (though they might have some we haven't discovered yet and vice versa) then math is a discovery, not an invention.

Well Mathematics is a Science. As such, it is not complete and may never be complete. Keep in mind that Newton had to develop Calculus, because existing mathematics simply wasn't up to the job. Also note that greater predictive precision requires inclusion of smaller and smaller perturbations. It is the lack of knowledge of all total influences on a system, which makes our math theories inaccurate with reality, let alone random influences which require stats!!Having said all this, I do hate when brilliant theories need to NORMALISE in order to yield useful results. This, to me, demonstrates that maths still has a long way to go.

P.S. Einstein used maths from a book which gathered dust on a library shelf for apx 60 years. Until Einstein used it, the maths it contained were considered quite interesting but of no useful application.

If gravity is an "outside force" then our math will never describe this reality because it is a computer simulation

The brain may be able to explain the brain. Similarly a computer simulation may be able to simulate that simulation (e.g. by mapping the time dimension into a space dimension or vice versa. A concrete example of this would be simulating a massive parallel construct in series. This requires far less computing power at the cost of a lot more time)

The only thing that is certain is that a simulation cannot simulate itself in realtime (e.g. the brain cannot fully grasp ALL that is going on in itself in realtime. But it could do so if it grasps parts one after another for a desired time interval.). So we'll never get something that will give us all the results for everthing all the time - continuously. But that is hardly needed.

"The brain may be able to explain the brain. Similarly a computer simulation may be able to simulate that simulation "

True but there are some problems according to Gödel's incompleteness theorems. In the article I mentioned> it is claimed that we can determine experimentally whether our world is a virtual reality. However, if that is the case then a full description of reality may never be available from inside the simulation. Think of the cave analogy in Plato. Actually, Plato never said a Platonic world provides a full explnation of everything. This is a misunderstanding of the author of the mentioned paper.

"The brain may be able to explain the brain. Similarly a computer simulation may be able to simulate that simulation "

True but there are some problems according to Gödel's incompleteness theorems. In the article I mentioned (http://www.digita...er-game) it is claimed that we can determine experimentally whether our world is a virtual reality. However, if that is the case then a full description of reality may never be available from inside the simulation. Think of the cave analogy in Plato. Actually, Plato never said a Platonic world provides a full explnation of everything. This is a misunderstanding of the author of the mentioned paper.

I have only seen 1 or 2 physicists (bordering on philosophers instead of actual scientists) on tv that are in agreement with Platonism. I have never actually met one. What every physicist or mathematician I've ever met thinks about this subject (including myself) is that calling math a universal language means exactly that. Language is used to describe something and communicate ideas between 2 people who might view the world in a different way. Language is information transfer. Math is just a system of describing what is happening. It is used to convey information from person to person so that everyone who looks at it can understand the physical process happening.

I think the good professor is wasting his time, because this should be (and mostly is) obvious. The only people that don't think this way are usually those who are trying to capitalize off of scientific philosophy; should read: popular science books/films.

The cricitism boils down to the simple realization that the map is not the territory.

In other words, while math can provide a perfect representation of reality like you can draw a perfect map, the perfect map would be a 1:1 replica of the territory, and as such would be perfectly useless.

What's so beguiling however is that all around us, we see inanimate matter performing precise mathematical operations. Thus therein lies the question; of whether there's any fundmanetal distinction between how WE process numbers, and how the universe does. Mathematical axioms certainly occupy a realm independent of physical constraints, yet the physical world appears bound by them all the same - arbitted by things like dimensional symmetries and conservation laws etc...

Our brain evolved to understand and navigate our environment and to interact with it efficiently to raise our chances for survival.Our logic and math came to be as our brain, generation after generation, formulated an approximation of the nature of reality in order to allow for better prediction and reaction to our environment. It is only an approximation, but it does aproximate reality, as if it wasn't we would have gone extinct.

Reality must be self consistent across all phases, times and scales. If this weren't so, inconsistent parts of reality would surely generate destructive effects that would have long since destroyed it. So laws of logic can change, but there must be some manner of logic. Since our math and logic was developed by a brain adopted to the "middle world" as Dawkins puts it, we may face challenges making sense of the quantum and galactic scale worlds. That's why the equations get long and convoluted. But they still work.

Reality must be self consistent across all phases, times and scales. If this weren't so, inconsistent parts of reality would surely generate destructive effects that would have long since destroyed it.

I'm not so sure about that. Inconsistent parts may simply 'split off' (multi world hypothesis?). And it's really only at the interfaces of consistent to inconsistent parts that you'd get any effects at all. So if inconsistency isn't fundamental - but 'occasionally allowed' - it may not be the demise of the universe.

(Note: I do think the universe is consistent. We havent observed anything that would argue otherwise. I just think it's almost impossible to prove it from within the universe)

Yah nou we have sat here before. I do not have to know how to speak philo to know that it is worthless. Just like you I rely on experts. Only my experts are scientists as yours are poets.

'Philosophy is dead.' -hawking'Philosophy is useless.' -Feynman'Philosophers make me laugh.' -Kraus'What is a Kant?' -most postdocs

Platonism is a metaphysical notion

Why because Plato is a dead philo? His theory of forms is an obvious absurdity. The use of the word is only an unfortunate symptom of the poison of religion. Philosophy was invented to wean intellectuals off god; a placebo. The metaphysical has no more validity than the hereafter, and is certainly no more useful to science as a concept.

It has absolutely no meaning whatsoever. As Feynman says, you can ask questions using such words to get any answers you want.

Mathematics is the architecture of pure logic. It gives us excellent models. Physical reality is ignorant of our models. It is up to us to choose the models we apply to different aspects of reality. P.A.M. Dirac's Quantum Mechanics is an excellent example of non-Platonic application. He simply summarized the observed characteristics of sub-atomic entities and their interactions, formalizing them in a customized mathematics. The model was designed according to the observation, and therefore must agree with them.Far too many modern theoreticians confound their beloved models with observed reality, and find themselves misled thereby.

Mathematics is the architecture of pure logic. It gives us excellent models. Physical reality is ignorant of our models. It is up to us to choose the models we apply to different aspects of reality. P.A.M. Dirac's Quantum Mechanics is an excellent example of non-Platonic application. He simply summarized the observed characteristics of sub-atomic entities and their interactions, formalizing them in a customized mathematics. The model was designed according to the observation, and therefore must agree with them.Far too many modern theoreticians confound their beloved models with observed reality, and find themselves misled thereby. Models are chosen by how well they IMITATE reality, but they are always just an imitation. The best models, such as general relativity, imitate reality very well.

I'd recommend to exclude the notions of philosophy from this discussion completely, as this fuzzy subject will not help you into coherent thinking very much (the reference of philosophers will just make this already sloppy discussion even more sloppier).

This entire discussion is a philosophical one. Logic is a branch of philosophy. Epistemology, the question of the nature and possibility of knowledge, is a philosophical one. While the core of QFT, QM remains validated via experimentation, it remains of interpretation of what the theory tells us about physical reality. IOW, interpretations of qm are philosophical.

Your theory of AWT is no more than philosophical musings if it is contingent upon intuition at the expense of lacking predictive power.

If you limit the meaning of 'mathematics' to 'mathematics based on the ZFC axioms, then the non-platonists are correct, because ZFC mathematics is incomplete and inconsistent in the universal domain (Godel's Incompleteness theorems), and because symbolic mathematics is a map (an abstraction) of a territory (existence), not the territory itself.

If you separate the symbolic representation of mathematics from the underlying mathematical structures and relations, and treat mathematics simply as a self-generating way to compose existence directly from the potential difference relations between energy and virtual energy fields, then the Platonists are correct.

Mathematics is 'unreasonably effective' because existence is a complete and consistent base ONE mathematical system that is based on the axiom of identity, instead of being based on predicate calculus, and the definition of the set membership, and set equality operators.

Yah nou we have sat here before. I do not have to know how to speak philo to know that it is worthless.

Your ignorance of philosophy is not an argument against it.

The philosophy of physics and the philosophy of mathematics ARE in fact legitimate branches of philosophy, irrespective of your personal aversion to them.

'Philosophy is dead.' -hawking

I proved to you in a previous thread that this quote is taken out of context. He was not speaking of modern philosophy of physics. In fact he has written on philosophy, in terms which coincide with what I post on the matter.

"There is no way to remove the observer us from our perception of the world, which is created through our sensory processing and through the way we think and reason. Our perception and the observations upon which our theories are based are shaped by a kind of lens, the interpretive structure of our human brains." - S. Hawking

But I only need to post one prominent physicist who disagrees to refute your claim, yet there are many;

"We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning." - Werner Heisenberg, Physics and Philosophy

"Any sound scientific theory, whether of time or of any other concept, should in my opinion be based on the most workable philosophy of science: the positivist approach put forward by Karl Popper and others" - Stephen Hawking.

"How does it happen that a properly endowed natural scientist comes to concern himself with epistemology? [..] Concepts that have proven useful in ordering things easily achieve such an authority over us that we forget their earthly origins and accept them as unalterable givens. Thus they come to be stamped as 'necessities of thought,' 'a priori givens,'" - Albert Einstein

-And your relative familiarity with some segments of it is no argument as to its relevance. How many philos dead and living would disagree with everything you say? Lots.

hawking was not talking about modern philosophy of physics

-Well of COURSE he was. He said that philosophy is dead BECAUSE it has failed to keep up with developments in science, specifically physics. What philos do you think he was referring to? Dead ones?

I only have to post one prominent physicist

-Really? Einstein said god does not play dice. Does this refute quantum physics? NO. Scientists often have moments of weakness and will tend to wax philosophical or poetic. And they do change their minds. And sometimes they go off the deep end like your buddy the consciousness-is-quantum-flux guy.

These wanderings may cause a stir in the philo world and in public perception but they have no effect on how these guys do their science.

There is a small fallacy here: the author is using the idea of "mathematics" when he should be using the idea of "model".

Whether or not mathematics have an onthologically independent existence (which I think it has not, what classifies me as a "non-platonist"), the contents of our models are far from being mathematical. Instead, we populate our models with our views of the World, our ideas, our preferences and our technical (and even personal) experience - that is what exists in our models and is written in mathematical symbols, which are ruled by the laws of Mathematics just as this text is ruled by the laws of the English Language.

Our models fail when our hypotheses and tests fail and they succeed when our hypotheses and tests succeed.

I didn't read everyones comments so sorry if this is repetative but, responding to the contents of the article, we didn't "invent" math, we invent the units of measurment and apply them. We do this in order to relate separate entities. From how many ounces or grams of cereal can be contained in a bowl to how many tesla over how much distance to accelerate a proton packet to a desired velocity. Yes we did invent symbols to represent numbers, but we didn't invent numbers....

I think the basic proof of what you and Abbott are saying is that you can't point to "5" in nature. You can point to a "quantity of 5", but there is no such than as a "5". Numbers are a concept and we only created them in order to understand the concept of limits. "Limits" being a concept which begins to break down when we move into quantum mechanics.

How could a person, like "professor" Derek Abbot, who has never been in real science, could evaluate Mathematics with such a generic conclusion? And what the heck does a non-scientific article doing here?

Noumenon, you're not a scientist and you even don't have a clue what a natural science is really about. Philos are a mirror of yourself - they say nothing essential with a lot of words. Just like politicians do.

Noumenon, you're not a scientist and you even don't have a clue what a natural science is really about. Philos are a mirror of yourself - they say nothing essential with a lot of words. Just like politicians do.

You don't know what your talking about, nor does your post contain any refutation of anything I stated here, just your dopy "opinion". I can't even tell whether you understood anything I wrote.

I think the basic proof of what you and Abbott are saying is that you can't point to "5" in nature. You can point to a "quantity of 5", but there is no such than as a "5". Numbers are a concept and we only created them in order to understand the concept of limits. "Limits" being a concept which begins to break down when we move into quantum mechanics.

Quantum mechanics seems to give a clear physical meaning to integers, as a number of quanta of energy, momentum, etc. Abbott's reference to continuum physics is ignoring this important point.

I think the biggest problem with the original article is that the question is worded ambiguously.

Is mathematics an effective way to describe the world?

Define "effective"

I think it wouldn't serve him to define too much. The above article doesn't even mention "predictions",.... obviously if a mathematical theory allowed one to make predictions, then clearly it is effective.

Noumenon, Franklins, Lurker2385, HannesAlfven - C'mon Zeph, you're still not banned here? And you're talking to yourself again and trying to mislead people that you know something about ANY science as usual, again. Do I really need to understand something from your bs?! Really?! Do you believe in yourself? :)

magnetic motors, cold fusion and similar stuffs which still have no coherent theory such an approach seriously slows down the progress, because many experimental results cannot be published - so that the people often believe, these effects don't exist at all and we're losing precious data about it

This might be the most important claim in the article. Part of the problem of our university system (and even websites/forums like this one) is that there is no ongoing effort to systematically catalog all of this claimed cherry-picking)

Scientists can find their reading/articles on nature.com ... etc. A layperson may not understand the systematical catalog, magnetic motors, cold fusion and similar stuffs. With Internet, are there some websites/forums where laypersons can find those systematic catalog, precious data and those experimental results which mostly are ineffectively mathematical applicable ?

This seems to be an unreasonable criticism. That math maps onto the universe does not mean that all the universe has to map onto math (i.e. that for every possible expression of a mathematical/physical theorem there has to be a corresponding reality...that would be Platonism)

Of course. Now for a question of philosophy: If a model is indistinguishable from that which it models, is there any difference between the two?I would argue no, and base my claim on the reflexive property. It would be like arguing over what the difference between 2 and the square root of 4 is. There may be different ways of modeling the object, including through the use of the thing itself, but they will all be equivalent.Q.E.D., the universe is mathematics. Or, perhaps more accurately, the universe is a subset of mathematics.

Quantum mechanics seems to give a clear physical meaning to integers, as a number of quanta of energy, momentum, etc. Abbott's reference to continuum physics is ignoring this important point.

If this is true then why do we run into the measurement problem and uncertainty principle? Quantification is our approximation of what is happening. It may just be that whatever is going on beyond that point has such an insignificant impact on our macroscopic experience that it isn't worth including such a fine (enormous) amount of detail in our macroscopic calculations and models.

Since mathematics is a human mental construct and humans are a contruct of the universe then mathematics is a construct of the universe, so what you are saying is the universe can't describe itself very well. :))

Quantum mechanics seems to give a clear physical meaning to integers, as a number of quanta of energy, momentum, etc. Abbott's reference to continuum physics is ignoring this important point.

If this is true then why do we run into the measurement problem and uncertainty principle? Quantification is our approximation of what is happening. It may just be that whatever is going on beyond that point has such an insignificant impact on our macroscopic experience that it isn't worth including such a fine (enormous) amount of detail in our macroscopic calculations and models.

When I say that "it may be", I mean that it is actually exactly what scientists do. If you can design a model that is correct 99.999999% of the time in our macroscopic experience of the universe, then you don't really need to quadruple the size of your calculation just to add a few more nines on the end of that unless you are proving a theory.

Back to the article: I'm wondering what else the author would like to suprcede mathematics (it's all well and good to say you don't like something - but as long as you have nothing better to offer that's not really a useful stance")

What it all boils down to is that we wish to draw information from observations. Now this is an inherent 'human bias', as a fully connected universe doesn't really do the information thing.

Information, at its core, requires a delineation into separate parts (and here's where the human bias comes in). This is required because humans have limited brain capacity - and we already do the delineation on the most fundamental level: the self vs. everything else.

So while math and information may not be the ultimate way of going about understanding the universe it IS the ultimate way if we stick to our human roots. (If we ever achieve unlimited brain capacity that may change - as then a holistic approach may be feasible)

Mathematics is an excellent tool for describing relatively simple systems and interactions, however it is less useful when it comes to complex systems and interactions, and the nuances of concepts related to esthetics.

Since mathematics is a human mental construct and humans are a contruct of the universe then mathematics is a construct of the universe, so what you are saying is the universe can't describe itself very well. :))

Lots of human mental constructs have nothing to do with the universe. Religion for one. Karaoke is another. So your word calculation is wrong.

As the brain is a machine we should eventually be able to reproduce any of it's functions with much more robust and dependable hardware. But why would we want to? Our thinking is just as flawed as the machine that does it.

BTW whole the application of formal models in physics is often motivated just with their "beauty" and "symmetry". The supersymmetry is considered relevant for physics, just because it's so "symmetric" - so far I didn't read any better reasoning of its existence.

The use of symmetry in physics is not motivated by aesthetic considerations as much as a purely mathematical result, in Noether's theorem.

It sounds strangely from person, who proposed the string theory here just before few years because it's so "elegant".

Well, since I never championed string theory you might want to get your head checked (and I seem to have told you this before).String theory is elegant - but that doesn't mean a thing as to whether it's true or not. When it starts making good predictions (and when the degrees of freedom are seriously collapsed) is when it'll become interesting.

The use of 'transparent' to define intuition is a bit redundant. Intuition means that one is able to form representations that are analogous to previous experience **. The question is why would this be possible for the qm realm, when it is clear we have evolved to synthesize experience only at the macroscopic realm. This is why qm is non-intuitive for example. History has shown that mind dependent intuition is too restrictive for physics to continue to make progress, at other scales.

** [or that is an a-priori form of thought necessary for experience given the nature of mind]

You see - so far I believed, that the Noether theorem is considered,just because it fits the experiments well. The "pure mathematical result" has no meaning as a motivation of theories for me at all...

Intuition means that one is able to form representations that are analogous to previous experience

Why not. In this sense the AWT relies on the oldest forms of experimental evidence - the behavior of multiparticle systems. It doesn't introduce the ad-hoced unknown yet particles like the etherons or fields. Which is necessary condition of really universal theory - the ToE based on untested yet assumptions cannot be considered a ToE, just because it relies on something which wasn't observed ...

You say AWT relies on particle systems, yet you also say that Quantum Mechanics and fields are nonsense. So AWT is correct because it's just like a particle system, but particle systems are nonsense. How could you ever be wrong with logic like that?

It's like you're angry at your spouse for snooping on your phone & finding nude pictures from an affair.

Exactly righten.wikipedia.org/wiki/Artifact_(error)Quote: "In natural science and signal processing, an artifact is any error in the perception or representation of any visual or aural information introduced by the involved equipment or technique(s)."

You say AWT relies on particle systems, yet you also say that Quantum Mechanics and fields are nonsense

I didn't say, that the QM or QFT are nonsenses. The nonsense for example is to consider the quantum fields as "nothing" and/or even deduce, that the Universe was formed from nothingness just because of it. But I don't negate the contemporary physics, I'm trying to explain it with common life analogies. This isn't a negation. I do want to reconcile their deductions with our real life experience instead.

Just because you don't understand it does not mean that it is incorrect. You are championing the idea of "Good Enough" because the path to a better future is too difficult for you to understand; whether or not you are aware that you don't understand is really the only thing up for debate.

Just because you don't understand it does not mean that it is incorrect

Of course, I can just subscribe it. BTW Are we talking about AWT?

because the path to a better future is too difficult

Nope, it's because we have too many confusing paths, which are getting blurred and fuzzy, which is typical behavior of http://www.aether...ent2.jpg inside of this continuum.But after then we get into social problems with theorists, who pursued whole life their personal ideas and who don't want to learn the new tricks, because they have already grants and postdocs contracted. Or because they're simply lazy enough and they don't want to lose their social credit.

What does it say when you try to save face by jumping to a conspiracy theory or abandoning the topic by jumping from quantum mechanics to astronomy? It says that your mouth is writing checks that your ass can't cash.

Or do you think, when Max Planck wrote that the "new scientific truth does not triumph by convincing opponents and making them see the light, but rather because its opponents eventually die", he had some conspiracy on mind?

Ah, Zeph, there only one eeny teeny problem with this profound thing ya say,,,,

Five generations have passed through the great halls of science since Lodge was on the scene,,,, so according to Planck's Law of Emerging Ideas things have gone amiss, because ya are the only one who got the memo about aether outliving it's detractors and taking it's proper place in science..

I laughed because it's just not true. A given volume of bananas would not condense into a black hole.

A banana weighs 0.125kg and has a density of 0.2 (much less than water).

r=2GM/(c^2) V=4π(r^3)/3=32(GM)^3/(3c^6) d=M/V=3c^6/(32G^3M^2) M=sqrt(3/(32G^3d))c^3 G~6.6E-11 m^3/(kg*s^2) d=0.2 g/cm^3=200 kg/m^3 c=299792458 m/s. Therefore a mass of ~7.2E39 kg with the same density as a banana in a spherical configuration would collapse into a black hole. This is only about 3.6 billion solar masses, there is observational evidence of black holes that are larger than this. This corresponds to ~5.7E40 bananas, though actual bananas would compress under the weight of those above, so it would not actually require quite this many (that said, I don't know where you could get this many bananas).

The simplest of math problems is addition. 1+1=2. Once you have given some names and symbols to these numbers then it would make sense they would add up like that.

1+1=1 when one uses modulo 1.

For my contribution to this discussion I define mathematics as the deduction of statements from axioms. Logic is a part of these axioms (the part that allows deduction). Which axioms one uses is determined by the statements one wishes to make. If the title of the article means "do there exist axioms from which all reasonably desired statements about physical observables can be deduced accurately in a reasonable amount of time", I would say that that is an open question. It is easy to infer from many successful cases of finding accurate models that such axioms exist, but there is no way to prove that any given set of axioms is the desired set (it is possible to disprove some sets if "accurate", "reasonably desired", and "reasonable amount of time" are well defined).

It is not clear that there is any such set of axioms and if there is it is not clear that it is unique (there may be many axiomatic systems that yield the desired results). Since it is only possible to try finitely many sets of axioms (assuming intelligence persists for a finite time) and finitely many physical observables and perform finitely many experiments, I think that "all" is not scientifically addressable. However, for a finite range of statements it may be possible (I would say that it almost certainly is possible for any experimentally accessible range and that the models generated are not unique).

Ya can not find the nuances without first doing the maths. Unless ya think "just a shade darker than fire engine red" is a proper scientific concept.

Actually, I do.

Sure, you can quantify the concept, "fire engine red." And you can quantify the concept, "a shade darker." But you can only do so under quantifiably defined and uniform lighting.

Even then, it's only an approximation, as the parameters of the receptor to perceive the reflected light isn't defined. The angle of incidence isn't defined, texture isn't defined... and so on. And once the standard, uniform lighting is taken away, all mathematical definitions become meaningless.

In this case, what we perceive as "a shade darker" actually retains more meaning in simple language than it does mathematically.

So in this case, which model of the world is actually more correct? The one with the well defined standards, or the aesthetic?

I'm sure with the understanding of the human brain that is available we can mathematically describe the neurons in a state of wonder. There is simply not enough room in this area to do so. Course we would also need the EEG of the state of wonder from whichever perspective it's ment.

Or as it's generally universally understood, we can simply and efficiently say, "a state of wonder."

And I dare say, you cannot convey the definition of the phrase mathematically, nearly so expediently. Ergo linguistic descriptors are more efficient in complex circumstances.

Isn't it obvious? ...Both. After all, beauty is in the eye of the beholder.

but that is not necessarily a repeatable and quantifiable answer. empirical evidence may be synonymous with the outcome of an experiment. In this sense, an empirical result is a unified confirmation and since you cannot have consensus on "beauty" then it is not an accurate descriptor. Just as "wonder" is defined by the observer, the answer would be malleable depending on point of view. the answer is too malleable and subjective

But as the concepts conveyed are generally and universally understood, it is. That is, it is self evident.

empirical evidence may be synonymous with the outcome of an experiment. In this sense, an empirical result is a unified confirmation and since you cannot have consensus on "beauty" then it is not an accurate descriptor. Just as "wonder" is defined by the observer, the answer would be malleable depending on point of view. the answer is too malleable and subjective

This is a good point. The logic is recognizably "fuzzy." But it's certainly more accurate than the same can be defined mathematically.

Frankly, these complex concepts cannot be explained mathematically in a compact enough form for the human mind to hold. However, linguistically, they fit right in.

You might as well be asking for mathematical definition of god. Can't happen.

That depends. I can mathematically describe the concept of God as follows: 1.

Or even in some cases: 1 + 1 + 1 = 1.

But what you probably mean to imply is there's no mathematical proof there is a god. This is correct. But equally so, there is no mathematical proof for most any emotional concept, yet generally, we all feel emotions and generally understand each other when we describe our emotions. Ergo emotions are real, yet not well defined by mathematical models.

. This is a good point. The logic is recognizably "fuzzy." But it's certainly more accurate than the same can be defined mathematically.

Frankly, these complex concepts cannot be explained mathematically in a compact enough form for the human mind to hold. However, linguistically, they fit right in.

you are forgetting that mathematics is the same all over, whereas linguistics has rules, semantics, grammar, syntax... all that crap, all subjective to the user, the language AND the year, as language use differs slightly between generations, and WIDELY over longer periods. that means it is malleable and abstract, unlike math. and therefor subjective, and cannot be considered empirical even though, right now, you may get the basic idea, but for how long?you cannot be specific enough to define the moment for all time without a universal language: mathematics IMO

"What I'm saying is, just because something is too complex to be conveniently stated mathematically, doesn't mean it cannot be expressed efficiently, at all."

but what you are also saying is that the complexity and convenience of language is subjective to the time, place, observer, period, dialect etc, etc... therefor it is NOT universal, and therefor mathematics is a better tool for passing on information (or describing things) in a universal manner that allows all parties to understand the concepts in the same way, at the same time, regardless of the time spread between speakers, language differences, etc. which is what the article asks! isnt it? what we want to communicate through the ages should not be "interpreted" as we interpret ancient Greek, Aramaic, etc. there will inevitably be flaws.

Once again, math is used to describe physical states. Not emotional aspects of an abstract idea.

So you're saying the wonder of a child holding a ladybug is not a physical state? How then might we ever progress to artificial intelligence, if we ourselves deny our consciousness is a physical state? How can we create that which isn't real?

And it's not just philosophical concepts that can't easily be explained mathematically, many complex physical systems are just as hard to describe. For instance, is the deformation of a rubber ball on a bounce better described mathematically, or with a single photograph?

pictures are often commonly mistaken for one thing or another... people even think that some pictographs/ glyphs represent "spacemen" in past times.but math is the same... we had NO problems interpreting the math from ancient times... it is the syntax and language that is all subjective. whereas symbols CAN be forgotten, math proofs are logic, pure and simple. and any steady investigation into the subject will give you the same results. that is why you can send math from one continent to another and it will always work out the same (as long as you use the same increments of measurement- metric and SAE dont always translate the same... because it is LANGUAGE the math is the same, the measurements are just due to language and abstract ideas of what is "better")

So now you're syaing thought itself is not a physical state (rhetorical)?

Even though it's rhetorical I'm going to take a stab at it. The abstract idea of thought is not a physical state. Now if you want to get into the workings of the mind then it's nothing more than an electrical state of the neurons in a brain. That electrical state can be represented with math. However, the questions remains due to lack of evidence, is that really what a thought is? Don't know yet. Until science can reproduce that exact state in another brain we will not have clear evidence of that.

You're all but admiting math fails in certain circumstances.

Isn't it interesting a complex thought itself can easily be defined and understood by all ,even though we don't understand the mechanics of it?

but what you are also saying is that the complexity and convenience of language is subjective to the time, place, observer, period, dialect etc, etc... therefor it is NOT universal, and therefor mathematics is a better tool for passing on information (or describing things) in a universal manner that allows all parties to understand the concepts in the same way, at the same time, regardless of the time spread between speakers, language differences, etc.

Math is only "universal" in that we set it up such that we perceive it that way. But even this fails, as our standards of measurements differ between cultures.

which is what the article asks! isnt it? what we want to communicate through the ages should not be "interpreted" as we interpret ancient Greek, Aramaic, etc. there will inevitably be flaws.

Isn't it interesting a complex thought itself can easily be defined and understood by all ,even though we don't understand the mechanics of it?

i understand your argument. i even agree with some of your points. but it also comes down to time... long stretches of time. something that "language" has proven to fail us. we can get a general idea of what is being said in our translations, but not a specific, logical all-encompassing detailed analysis and comprehencive translation of the idea in question. Math does transcend that issue, and HAS... and i also believe that all things, given time, will be mathematically explained. it is the blessing/curse of humans to break things down into the simplest, most logical definition.

pictures are often commonly mistaken for one thing or another... people even think that some pictographs/ glyphs represent "spacemen" in past times.but math is the same... we had NO problems interpreting the math from ancient times... it is the syntax and language that is all subjective. whereas symbols CAN be forgotten, math proofs are logic, pure and simple. and any steady investigation into the subject will give you the same results. that is why you can send math from one continent to another and it will always work out the same (as long as you use the same increments of measurement- metric and SAE dont always translate the same... because it is LANGUAGE the math is the same, the measurements are just due to language and abstract ideas of what is "better")

All of which make math a great tool for describing relatively simple systems. But it simply can't, from a practical standpoint, adequately describe complex systems.

"Math is only "universal" in that we set it up such that we perceive it that way. But even this fails, as our standards of measurements differ between cultures."

no... math is math. cubit and feet are units of measure, and subject to definition, but 1+1 will always be 2 , whether you use cubits or feet. the difference between cultures are because of ideology and language ... not because of math. math is the same across the board.

i understand your argument. i even agree with some of your points. but it also comes down to time... long stretches of time. something that "language" has proven to fail us. we can get a general idea of what is being said in our translations, but not a specific, logical all-encompassing detailed analysis and comprehencive translation of the idea in question.

Well that's arguable, on a case by case basis. Even so, English is generally becoming the scientific standard.

Math does transcend that issue, and HAS...

I disagree. Just because we figured out some ancient symbols, doesn't mean that we have and will always be able to interpret other culture's mathematical symbols.

and i also believe that all things, given time, will be mathematically explained. it is the blessing/curse of humans to break things down into the simplest, most logical definition.

"All of which make math a great tool for describing relatively simple systems. But it simply can't, from a practical standpoint, adequately describe complex systems."the limitations of our understanding are just showing. my 9 year old grandson has some girls he "likes", but cannot adequately describe what he actually feels... our understanding of math is the same. just because we are in our "terrible two's" , or whatever, does not mean there is a limitation to math, because math is pure logic, and in time, it will be able to adequately communicate whatever we wish through a universal set of logical steps. this is the power of math (as much as i hate it). the power to describe logically over spans of time. this is what makes an effective tool. that is my argument, that it will be the most effective tool over time, because it HAS been the most effective tool over time.

Sure, some people might look at it that way. However, if you had read all of my post you would have seen that's not really the case.

Which only serves to bring us back to the beginning. Is mathematics an effective way to describe the world?

You feel the answere is always yes, I feel the answer is only sometimes.

Isn't it interesting a complex thought itself can easily be defined and understood by all ,even though we don't understand the mechanics of it?

That is what language is good at, but unless it gets translated it can't be understood by lots and lots of people. Keep in mind though sometimes there isn't a direct translation. Have you ever heard the phrase. Looses something in translation? Which is why in many fields and applications, language has been (and is being) standardized.

"Math is only "universal" in that we set it up such that we perceive it that way. But even this fails, as our standards of measurements differ between cultures."

no... math is math. cubit and feet are units of measure, and subject to definition, but 1+1 will always be 2 , whether you use cubits or feet. the difference between cultures are because of ideology and language ... not because of math. math is the same across the board.

This is not correct. Even 1 + 1 does not always necessarily equal 2. For instance, 1 particle plus one antiparticle, equals what, exactly?

sorry. still math logic.... and it would be 1-1 which is 0. one is positive, one negative, and they cancel each other out. or you could write it (pos) 1 plus a (neg) 1 which equals zero... same same.

But this is true only when you literally bring them together. Generally speaking (supposing Einstein was right), one antiparticle is in every way equal to a particle, when separated. So if I have one particle and one antiparticle, I have 2 particles. But if I combine them I have nothing?

However, it would sure be interesting if it turns out antiparticles have antigravity properties...

sorry... nice try, though... still the same answer. keep them separate, and you still have a positive and a negative. their absolute value may be one and one, but only if counted individually, and separately. when combined, they will always be a negative 1 plus a positive 1 equaling zero.

sorry... nice try, though... still the same answer. keep them separate, and you still have a positive and a negative. their absolute value may be one and one, but only if counted individually, and separately. when combined, they will always be a negative 1 plus a positive 1 equaling zero.

as for anti-particle properties... I would love to know more. :-)

Supposedly, the gravity/mass/energy of an antiparticle is the same. That is, an antimatter body and a matter body can technically orbit each other and share a gravity well. The combined mass can then technically be towed around, as if it were a combined mass of two ordinary matter bodies (1 + 1 = 2). Do you see the conundrum?

well, i am not a physicist, but form everything that i have read, anti-particles and particles will seek each other out and mutually annihilate, therefor the argument is not a conundrum. if a particle exists with an anti-particle, they will seek each other out and you get zero again... i wonder what a physicist would say about that though... perhaps a particle and an anti-particle orbiting a sufficiently large mass that could keep them separate. the kicker would be keeping them separate... that is the only way you could count them both. the absolute value would be two but the combination is still zero.

It is easy to agree with Abbott on the general issue. (Personally my analysis has concluded the same long since.) The empirical null hypothesis is that mathematics is a human construct, because historically it is.

So platonists et cetera philosophers needs to test their ideas of something more.

There is a recourse to a testable constraint of Tegmark though. He posits that a multiverse where mathematical objects (theories) is the universal substrate would be a simpler hypothesis. In his hypothesis mathematics (perhaps only sometimes) maps to physics, especially where we live. He argues for the identity mapping as the simplest. This would presumably be tested if selection bias (weak anthropicity) can be tested valid and with the testable exclusion of everything else.

But compared with the empirical null hypothesis it isn't simpler, because Tegmark doubles his objects. Mathematical objects is a class, physical objects is another, and he sets up a mapping in between even if he chooses the identity mapping. One way to interpret it is that they have different properties before merging - physics is testable, for one. So this fails too, whether it is testable or not.

Subjects in and of themselves are self defining things. Keys hide in no one thing.

Is that nonsense or does it accurately describe some phenomena? As our measuring tools improve and our statistical correlations of data increase we will find the crease within the singularity or perhaps the empty set {} that is the nature of all or nothing. Anticipate, believe, but do not expect my fellow discoverers. Tolerate exploration on all frontiers and assist those you can in finding the universe's or perhaps multiverse's gears. She will sing to us if we but seek the time/space...... Nothing is impossible. I'm possible and so are you. We will be... The self knowing mind whether it is self, society, or some construct others refer to as God is unfolding. :)

This article is very subpar, and some of the comments are absolutely horrendous. Cherry picking mathematics and the fact that our human timescales may distort the actual truth are not adequate refutations of the idea that the universe is inherently mathematical (or that it has a structure that we can exemplify through mathematical models). For one, different structures have different mathematical properties, so the fact that group theory, number theory, and calculus all apply to different features of the world does not mean we have "cherry picked" our way into describing the world.

In addition, it could be that the universe vanishes 5 minutes from now, even though our models don't predict any such occurrence. It would be extremely embarassing, however, to claim that this possibility makes it highly likely that our models are wrong. Just so, mathematics might not describe the universe adequately in some ways, but as of now, is has passed all the tests. Platonism for the win.

By the way, people need to stop using modular arithmetic to claim that 1+1 = 0 and other such nonsense. Its actually supposed to be a congruence relation, so stop using it to prove your crackpot ideas or try to suggest some sort of inconsistency in the mathematical edifice where none exists.

To describe universe there are many ways. Mathematics one of them. Is math an effective way? One can describe it by photographing it. Bird, moon, Jupiter, galaxies and black holes. All can be 'put' in one photo of proper size. Then you'll understand the problem. Zoom in/out to certain views still ok containing (all of) them. A ((note:)whole) bird viewed in detail doesn't mean the picture without Jupiter and galaxies, theoretically Jupiter & galaxies are still in picture perhaps they only occupying no pixel, due to different exposure time sensitivities etc. And picture does not know the other side of moon Jupiter etc. Another point, picture is math nevertheless. Then, with picture or math is much effective than without it. The % or how effective is it, are there other effective ways? are other problems.

he argues for the opposing viewpoint, the non-Platonist notion that mathematics is a product of the human imagination that we tailor to describe reality

when you recognize that math is just a mental construct

'a product of the human imagination' & just a mental construct? I don't understand, human effectively links mathematics and world, different persons at different places and time can find same answers/numbers.

will break down at some point because perfect mathematical forms do not exist in the physical universe - then you can see how ineffective math is

.. some of the comments are absolutely horrendous. [...] the fact that our human timescales may distort the actual truth are not adequate refutations of the idea that the universe is inherently mathematical (or that it has a structure that we can exemplify through mathematical models). [...] Platonism for the win.

What is rather horrendous is that seemingly scientifically minded people fall for such metaphysical fallacy as Platonism.

It makes zero rational sense to suggest that the universe is intrinsically 'mathematical', independent of its conceptualization in thought. That's what would qualify as Platonism,... ontologically independent of thought.

The universe of itself (noumenal reality), does not have need of relating things, nor of measuring things, nor of redundently constructing models of itself. Mathematics therefore does not exist in any fashion independent of mind asking such questions.

It is why Einstein had to take an Operational pov with general relativity.

Stupidest most nonsensical article I have ever read on physorg (and there have been some pretty bad ones before this).

Since when does using the right tool for the job become cherry picking? Having a set of wrenches, why would I try to build a computer? No, I'd just cherry pick the loose nut jobs and the real nut jobs could publish an article on the ineffectiveness of wrenches.

Math is a modeling language, and is as good as the understanding of what it is being used to model. Models are created with inherent limitations. The limitations are either in understanding of what is being modeled, or a result of the size/complexity of the problem,or the suitability for matematical modeling.

Even counting has its limits. When counting bananas, for example, at some point the number of bananas will be so large that the gravitational pull of all the bananas draws them into a black hole. At some point, we can no longer rely on numbers to count

WTF?

Obviously, this EE forgot to use probability to count the bananas instead of using an accountant ;P

I don't think a universe need necessarily be mathematical. However, the universe which was created, in which we actually exist, is definitely mathematical.

Does math describe everything in our universe? Maybe. Maybe not. We'd need to know everything, or at least nearly everything, about our universe in order to answer the question absolutely.

All known phenomena seem to be describable in some form of mathematics.

Yet it is possible to prove that it is mathematically impossible for a temporal being or civilization to ever know everything about our universe. For starters, just imagine how many molecules are required by our brain to store memory of the location of just one molecule. Obviously you can't map the location of everything in the universe, because you can't make a memory large enough; even if you only hit the high notes, I doubt Earth could store a map of every star and planet in the universe.

The universe of itself (noumenal reality), does not have need of relating things, nor of measuring things, nor of redundently constructing models of itself. Mathematics therefore does not exist in any fashion independent of mind asking such questions.

If math does not exist how do objects "know" how much force (or space-time warp,etc) is being applied to them by gravity or other forces?

Our universe would not exist as it does without mathematics being a part of it's very construction.

The fact that the universe can contain intelligent beings such as ourselves, who are then able to produce self-referencial models of both themselves and the universe, should tell you something.

The universe is created by a mind, so it comes as no surprise that it would bear the markings of a mind.

If it looks like a mind, and acts like a mind, then it probably is a mind, or was created by a mind.

The universe of itself [...], does not have need of relating things, nor of measuring things, nor of redundently constructing models of itself. Mathematics therefore does not exist in any fashion independent of mind asking such questions.

If math does not exist how do objects "know" how much force (or space-time warp,etc) is being applied to them by gravity or other forces?

It would be redundant for an object to be both itself and to be it's own model of itself. That is what "to know" means afterall, ... to reproduce reality in an abtract conceptual form. Reality apart from mind knows nothing, it just is. Like space and time, mathematics are not entities existing independent of their application in relating and ordering things. Platontism is metaphysics.

It would be redundant for an object to be both itself and to be it's own model of itself. That is what "to know" means afterall, ... to reproduce reality in an abtract conceptual form. Reality apart from mind knows nothing, it just is. Like space and time, mathematics are not entities existing independent of their application in relating and ordering things. Platontism is metaphysics.

You don't understand the question, though you thought you did.

If mathematics is not "real" then the inverse squared relationship would not exist. Why would the objects' orbits exist, if they were not being pulled with a precise force, or following a precisely warped path?

You have a model of yourself, and we call this model the "self image" it is a combination of what you know and what you believe about yourself.

However, as regarding inanimate matter, I used the word "know" generically in a sense that did not require self intelligence.

They represent the larger mass and the smaller mass (though they can be equal), and "r" means something as well, namely the distance between them.

Change any one variable in the formula, and the opposite mass "feels" less or more force, accordingly, referencing Newtonian Dynamics anyway.

How would you express that fact, which we know to be true, without using mathematics?

If the observation and the mathematics are identical, or at least nearly identical, then it stands to reason that the universe is mathematical.

Are you claiming that all similarities between mathematical models and the universe itself are coincidental?

The mathematical model works because the universe is mathematical.

Math isn't something humans made up, it was discovered by man, not invented by man, though formal language has standardized it into what we call mathematics today. The relationships always existed; to say otherwise is completely absurd.

"You cannot describe something infinite (true infinity in space and time) in a finite amount of time.""You therefore cannot describe the universe in any language.""Furthermore, you cannot describe something infinite (true infinity in space and time) in math because in math whatever you describe has a focus (is finite), and the universe is infinite."

"You cannot describe something infinite (true infinity in space and time) in a finite amount of time.""You therefore cannot describe the universe in any language.""Furthermore, you cannot describe something infinite (true infinity in space and time) in math because in math whatever you describe has a focus (is finite), and the universe is infinite."

There is no evidence to suggest that the universe is infinite in either space or time.

The second law of thermodynamics forbids the universe to be infinite in time, because it would have already reached a state of maximum entropy.

The universe can't be infinite in space, because growing to that size would require an infinite amount of time.

When you don't understand math even the simple equations become complex.

I'm sorry you're having difficulty understanding it. It's simple really. According to Einstein, antimatter particles are just like matter particles, except they have opposite charges. Whereas gravity affects both the same way and both carry the same mass. So they behave like one great mass in a shared gravity well (1 + 1 = 2) but annihilate when combined (1 + -1 = 0).

Was that too complex for you still, or are you getting it?

hmmm that's odd, we can create black holes that will suck up the whole earth but we have no affect on the climate. Interesting premise. Completely crazy of course but interesting in a neurological kind of way.

That is correct, however, that is not what you said. Here is what you did say

1 + 1 + 1 = 1

and

Even 1 + 1 does not always necessarily equal 2

Both of these statements are completely incorrect. Making the normal base 10 assumption.

This is a matter of interpretation. As I did not define the 1's in the 1 + 1 + 1 = 1, it's entirely valid as 1 thing + another thing + a third thing can comprise an entirely different thing.

Even when dealing with particles of matter and antimatter. Antimatter by definition is a negative. Therefore, you equation should have been 1-1=0 or -1+1=0 or maybe |1|+|1|=2 as has already been explained to you. I thought you had understood. Judging by your correction of the formulas I see you did.

This gets downright metaphysical: If I own one matter apple and one antimattter apple, Do I own two apples ...or nothing?

My statement was perfectly correct. When you don't understand math even the simple equations become complex. I'm glad you now understand the math behind it so you don't make any more erroneous equations.

I put the minus sign in to clarify the reaction, but technically I could have stated the denominators stood for mass, and it truly would have been 1 + 1 = 0.

Once again, my statement is completely correct. There would have to be some kind of neurological disorder (crazy for short) to not see the failure of the logic. You see this as bullying, I see it as calling a rock a rock.

So it's your contention that if you don't understand the logic it's necessarily bad?

Can you give me a example of this? I've never seen it, read it, nor can I conceive of one instance where this could possibly be true.

Sure. One blanket + one basket of food+ one sunny day = a picnic.

Even when dealing with particles of matter and antimatter. Antimatter by definition is a negative. Therefore, you equation should have been 1-1=0 or -1+1=0 or maybe |1|+|1|=2 as has already been explained to you. I thought you had understood. Judging by your correction of the formulas I see you did.

This gets downright metaphysical: If I own one matter apple and one antimattter apple, Do I own two apples ...or nothing? You would have two apples if the do not come into contact with each other. This is where the |1|+|1|=2 comes in. There is not anything metaphysical about it. It's pretty straight forward math. It's still 1 + 1 = 2. The special separators are irrelevant, especially when simply discussing the mass.

I put the minus sign in to clarify the reaction, but technically I could have stated the denominators stood for mass, and it truly would have been 1 + 1 = 0.

That is where the absolute values come in.

The mass of one is exactly equal to and therefore transposable to the other. Therefore, (as you've just admitted) I was entirely correct in stating 1 + 1 can equal 0.

So it's your contention that if you don't understand the logic it's necessarily bad?

Yes, if someone can't understand logic they are either refusing to think or have a neurological disorder. When people refuse to think they agree to be dumbasses. An accrual neurological disorder might be treatable but at least understandable.

So you're admitting then that since you didn't understand my logic, you're either a dumbass or you have a neurological disorder?

Does it ever occur to you that maybe, sometimes, people just misunderstand the issues?

First off JohnGee was the one the made the statement I commenting on. Rather it had anything to do with you is beyond my point. Second, I don't claim there wasn't an insinuation, their clearly was. However, it was not directed at you. Simply the statement JohnGee had made. Third, I have no knowledge of your beliefs on the topics so how could I be directing at you?

JohnGee's response was clearly in reference to me, therefore your followup, in context (intended or not), refers to me.

What name did I call you? I don't see any name calling on this article from me at all. Any perceived innuendo or aspersions was from a comment I made in regards to someones else's assertion. You say the assertion wasn't correct, then my comment didn't have any bearing on you.

The mass of one is exactly equal to and therefore transposable to the other. Therefore, (as you've just admitted) I was entirely correct in stating 1 + 1 can equal 0.

this is not a matter of adding masses, but objects. what you are confusing is the object and the negative object... and absolute value. either add absolute value or not.

Does it ever occur to you that maybe, sometimes, people just misunderstand the issues?

this is a simple situation of misunderstanding. you are not understanding basic math or science, and are using a metaphysical or semantic argument (depending) to get your point across. there is no magic. just logic. 1+1 only equals more than two when the condom breaks. and that is biology, not math

And this is exactly why you can't things that are not alike. One of the first fundamentals in math.

Which only serves to demonstrate that math isn't always the best model for the universe,as most things are made from many disparate parts.

It's still 1 + 1 = 2. The special separators are irrelevant, especially when simply discussing the mass.

That is because you are using the absolute values which is indicated by |1|

No, when i'm discussing the mass, as the sign for the mass in either case is normally positive, I technically don't need to use the absolute value to write the formula. And absolute values when added, do not sum to zero (at least they're not suppose to).

and like rug says... you cannot add things that are not alike. you can only add the absolute value of those things, or bring those things into equality.matter and anti-matter are NOT the same, one is Pos, one Neg. but their absolute value is always Pos, therefore it MUST be EITHER 1+1=2 OR -1+1=0

The mass of one is exactly equal to and therefore transposable to the other. Therefore, (as you've just admitted) I was entirely correct in stating 1 + 1 can equal 0.

This is not correct. Due to the fact one is a negative charge so you must use a negative value.

As I might not even know one body is antimatter, the charge is clearly irrelevant to the mass, and as I'm calculating only the mass, the math (as we might normally use it) can fail.

You're logic was flawed. No one can understand flawed logic.

My logic is impeccable.

That does seem to be the case with you currently. It happens all the time and is not a big deal. However, when that misunderstanding is cleared up and yet the person still perpetuates the misunderstanding then my original statement is clearly case.

But you're the one perpetuating the misunderstanding, therefore your statement must apply to you.

you can only add the absolute value of those things, or bring those things into equality.matter and anti-matter are NOT the same, one is Pos, one Neg. but their absolute value is always Pos, therefore it MUST be EITHER 1+1=2 OR -1+1=0

your logic is based upon a lack of understanding of the known laws of physics, therefore is flawed from the beginning. and it is because you chose to use the anti-particle. in your mass argument, you do state two particles (one the anti-particle of the other) orbiting a suffucient mass (paraphrased).for get about mass for a moment. in our current known universe, and from observation and testing, form everything i can read, i dont think even a black hole would be able to separate the particles enabling them to co-exist. especially since we live in a universe populated by matter, and not anti-matter. there could not be the ability for an anti-particle to exist without interacting with normal matter. then there is the whole quantum mechanics thing... even empty space does not have a zero charge...

@ubavontuba - Nothing stated here has been any higher than pre agrabah level. You obviously have higher education then that, no malice intended. However, it's clear you have not retained a few fundamentals.

It's clear you want math to work properly in all cases. I'm only pointing out there are special cases where the math (as we know it) doesn't map well to the possible reality. In this one simple case, without knowing one mass is antmatter, we can be completely fooled by the math.

After this long discussion with your clear misunderstanding after being corrected multiple times from more than one person I am forced to end the discussion. I refuse to argue the logic about illogical statements.

I suppose that not understanding the logic certainly would make it appear illogical...

sigh* but you CHOSE to use the ANTI-particle, because you thought it would help your argument. therefore my logic stands. and you are wrong.

Now you're confusing charge with mass.

again... not confusing it at all. just using YOUR argument ... mass is NOT the issue. anti + reg matter was the logical issue, and again, I stand by my argument.

this is miscommunication. I am trying to talk math and science, you are trying to invent a hypothetical situation to support your belief. not the same thing. apples and oranges. we will not be able to come to any agreement.

your logic is based upon a lack of understanding of the known laws of physics, therefore is flawed from the beginning. and it is because you chose to use the anti-particle. in your mass argument, you do state two particles (one the anti-particle of the other) orbiting a suffucient mass (paraphrased).for get about mass for a moment. in our current known universe, and from observation and testing, form everything i can read, i dont think even a black hole would be able to separate the particles enabling them to co-exist. especially since we live in a universe populated by matter, and not anti-matter. there could not be the ability for an anti-particle to exist without interacting with normal matter. then there is the whole quantum mechanics thing... even empty space does not have a zero charge...

A valid point. My scanario certainly is unlikely to occur in the known universe, but who can say if what we don't know about the universe poses similar problems for our math?

your logic is based upon a lack of understanding of the known laws of physics, therefore is flawed from the beginning. and it is because you chose to use the anti-particle. in your mass argument, you do state two particles (one the anti-particle of the other) orbiting a suffucient mass (paraphrased).for get about mass for a moment. in our current known universe, and from observation and testing, form everything i can read, i dont think even a black hole would be able to separate the particles enabling them to co-exist. especially since we live in a universe populated by matter, and not anti-matter. there could not be the ability for an anti-particle to exist without interacting with normal matter. then there is the whole quantum mechanics thing... even empty space does not have a zero charge...

A valid point. My scenario certainly is unlikely to occur in the known universe, but who can say if what we don't know about the universe poses similar problems for our math?

sigh* but you CHOSE to use the ANTI-particle, because you thought it would help your argument. therefore my logic stands. and you are wrong.

I'm talking about mass and you can't get your mind off of charge. How is this my fault?

again... not confusing it at all. just using YOUR argument ... mass is NOT the issue. anti + reg matter was the logical issue, and again, I stand by my argument.

I guess i should have simply described two masses in orbit, and not told you one was antimatter until much later then?

this is miscommunication. I am trying to talk math and science, you are trying to invent a hypothetical situation to support your belief. not the same thing. apples and oranges. we will not be able to come to any agreement.

[p]A valid point. My scenario certainly is unlikely to occur in the known universe, but who can say if what we don't know about the universe poses similar problems for our math?[/p]

this is the realm of science fiction, not science fact. and even given two masses in orbit, it is still 1+1=2 until you put a charge into them. period. in order for your argument to work it MUST be science FICTION because when two masses orbit, which occurs regularly, they are 1+1=2. when you state, for ANY reason that one is an anti-particle, then regardless of mass, charge comes into play. because one is the OPPOSSITE of the other, therefore a NEGATIVE. mass is not the issue in this case anymore. the fact that the anti-particle cannot co-exist with the particle becomes the issue. you should have kept with the interpretation of math as a language, in such instances, semantics can and would have been great. you simply chose an issue that you did not fully understand.

this is the realm of science fiction, not science fact. and even given two masses in orbit, it is still 1+1=2 until you put a charge into them. period. in order for your argument to work it MUST be science FICTION because when two masses orbit, which occurs regularly, they are 1+1=2. when you state, for ANY reason that one is an anti-particle, then regardless of mass, charge comes into play. because one is the OPPOSSITE of the other, therefore a NEGATIVE. mass is not the issue in this case anymore. the fact that the anti-particle cannot co-exist with the particle becomes the issue. you should have kept with the interpretation of math as a language, in such instances, semantics can and would have been great. you simply chose an issue that you did not fully understand.

But that's what i'm getting at. The language of math isn't always sufficient to map everything. Knowing the mass certainly doesn't mean you know the charge.

ubavontubawe seem to be at an impasse. you do not understand, or perhaps just refuse to capitulate to lack of knowledge about certain science issues, and i am trying to explain, but obviously i am failing. i am not able to sufficiently explain to your liking and therefore this discussion is not capable of progressing. You are arguing semantics and science fiction, not math and logic. whereas there are times when there can be a lack of knowledge, i have tried to explain it above, to the best of my ability. i apologize for the inconvenience, i am a simple mountain man, not a physicist.PEACE

ubavontubawe seem to be at an impasse. you do not understand, or perhaps just refuse to capitulate to lack of knowledge about certain science issues, and i am trying to explain, but obviously i am failing. i am not able to sufficiently explain to your liking and therefore this discussion is not capable of progressing. You are arguing semantics and science fiction, not math and logic. whereas there are times when there can be a lack of knowledge, i have tried to explain it above, to the best of my ability. i apologize for the inconvenience, i am a simple mountain man, not a physicist.PEACE

No need to apologize. I feel equally frustrated by my inability to clarify my point. But in the larger scheme of things, i guess it doesn't really matter.

If mathematics is not "real" then the inverse squared relationship would not exist. Why would the objects' orbits exist, if they were not being pulled with a precise force, or following a precisely warped path?

Actually it is you who don't understand the difference between knowing something, requiring a mind in conceptualizing it, and the thing as it exists in itself. Conceptualizing reality with use of mathematics is a human endeavor. Yes 'phenomenal reality' is mathematical but only because by definition it contains a mind dependent component.

Change any one variable in the formula, and the opposite mass "feels" less or more force, accordingly, referencing Newtonian Dynamics anyway.

How would you express that fact, which we know to be true, without using mathematics?

Exactly, you couldn't EXPRESS that fact independently of knowledge. Expressing facts is what mathematics if for.

Math isn't something humans made up, it was discovered by man, not invented by man, though formal language has standardized it into what we call mathematics today.

Platonism is pure metaphysics. Metaphysics has no place in science. I'm not exactly suggesting that mathematics is 'made up' subjectively....

I mentioned epistemology above somewhere,... in the study of what knowledge IS and how the mind acquires it, one could say that mathematics (& space and time, etc) are a-priori forms of thought, a hardwired means of ordering experience given the nature of mind and how mind operates on experience.

This is why such concepts SEEM like their "real" even though they are not tangible. It is very hard to get out of our own intellectual way. Even among pure mathematicians it is not clear and there is widely differing camps about this subject. IMO it, along with why qm is non-intuitive, will remain unclear until we understand how the mind works itself,..

.... after all, given our nature we could not help but believe that such notions as locality, counterfactuality, space, time, separability and determinacy,.. are as Platonically "real" as mathematical Ideas,... but in fact at the qm scale they fail to order that experience in accord with such "classical" intuitions.

This is a Physical discovery, that some of our concepts must then be artifacts of thought, and NOT a real structure existing independently of mind. In QM there is a discontinuity between the mathematical formulation and an observation,... in fact measurement in some way produces the result that was not there before hand, the wavefunction is a collapse into concepts.

If mathematics is not "real" then [...] Why would the objects' orbits exist

Relationships don't exist as things independently of us, nor do paths. They're questions about things and where things will be expected at next observation, not things in themselves independent of observation.

But at the water surface the surface ripples do follow the inverse law just at the certain distance - at too small and too large distances this law becomes violated with scattering and nothing strange is about it. In the same way the dense aether model perceives the limitation of low-dimensional math (models) inside of observable Universe. It indeed works well - but just at the certain distance/energy density scale - that's all.

Zeph, thank ya for my morning dose of water rippling through the aether on low-dimensional surface model (maths). As edifying as always.

But if I may digress for a moment. In October I'll be visiting your neck of the water surface (so to speak) and was wondering if we might get together for a pint and discussion face to face on the deeper issues confounding modern physics. I don't know if ya are close to Plzen, I'm going there, but would be happy to make a side trip.

Even counting has its limits. When counting bananas, for example, at some point the number of bananas will be so large that the gravitational pull of all the bananas draws them into a black hole. At some point, we can no longer rely on numbers to count.

Yes, bananas sums up this work quite well.

One example is an improvement of vector operations. The current method involves dot and cross products, "a rather clunky" tool that does not generalize to higher dimensions. Lately there has been a renewed interest in an alternative approach called geometric algebra, which overcomes many of the limitations of dot and cross products and can be extended to higher dimensions.

Lots of human mental constructs have nothing to do with the universe. Religion for one. Karaoke is another. So your word calculation is wrong.

I think you have that exactly backwards. Think of a concept that has nothing to do with the universe, and you will be the first. Even the impossible, including the paradox, all comes from our universe (virtual particles, particles existing in two places at once, concept of zero which doesn't actually exist, etc).

There is no absolute reality.Only what we ourselves can comprehend of nature (by examining it) is what we understand to be what actually exists. Consequently, because it is in our minds, these same minds are our sole means for understanding it. Our best tool for this surely is mathematics and therefore mathematics is the only way we will ever be able to use science in an analytic sense to understand our natural surroundings and enviroment.

"You cannot describe something infinite (true infinity in space and time) in a finite amount of time.""You therefore cannot describe the universe in any language.""Furthermore, you cannot describe something infinite (true infinity in space and time) in math because in math whatever you describe has a focus (is finite), and the universe is infinite."

What about a circle? or a sphere? Circumference is an infinite distance which can only be described by an infinite number (pi) which is the result of a mathematical relation. Sounds like Math wins again.

I'm sorry but anyone who says mathematics is ineffective in describing the world is just talking nonsense I don't care what their credentials are. The author of this piece is obviously confusing mathematics with models. Yes models are limited but mathematics is not. Mathematics allows for the continual refinement of models. The fact the author seems to be unaware of the difference is telling. I've heard this argument before. Some people used to use the example of mountains to make the claim mathematics can never really describe the world because they are not perfect cones. Then fractals was discovered and destroyed that argument. These people remind me of creationists who spout nonsense like, "if evolution is true how come you never see monkeys give birth to humans?" Complete idiocy. The world is either rational or it isn't. If it is then mathematics must be effective. If it isn't we should all just give up and let the mystics take over because that's the only alternative

"You cannot describe something infinite (true infinity in space and time) in a finite amount of time.""You therefore cannot describe the universe in any language.""Furthermore, you cannot describe something infinite (true infinity in space and time) in math because in math whatever you describe has a focus (is finite), and the universe is infinite."

What about a circle? or a sphere? Circumference is an infinite distance which can only be described by an infinite number (pi) which is the result of a mathematical relation. Sounds like Math wins again.

I'm sorry but anyone who says mathematics is ineffective in describing the world is just talking nonsense I don't care what their credentials are. The author of this piece is obviously confusing mathematics with models. Yes models are limited but mathematics is not. Mathematics allows for the continual refinement of models.

This is just the point. The models must apply to our world, the math must not. Nobody says, that the math is not effective in, well, describing of itself...

What??? How do you figure models must apply to the world but the mathematics used to construct and refine them must not? That makes no sense whatsoever

The most compelling evidence math is effective in describing the world is the fact different cultures arrived at the same conclusions regarding it. The symbols they used were different but the principles they discovered were identical

The most compelling evidence math is effective in describing the world is the fact different cultures arrived at the same conclusions regarding it. The symbols they used were different but the principles they discovered were identical

@AlumnodeVerum - this is the heart of my argument! thank you, very well said.

@teech2

[p] On the other hand the mathematics doesn't allow model even the system of six gravitating bodies in deterministic way - such a system is too complex for it. [/p]

like rug says - just because WE cant do the math, doesn't mean the math is not capable. besides, what more is there to learn that we don't know?

really? "in numerology and cabala the math is literally unbeatable" i am not sure how you can make that statement with a straight face... prove to me the math is "literally unbeatable"... please.

and i stand by my arguments posted above... please READ THEM ALL above before coming back to me on that, unless you can prove something with numerology that i need to know. i am not arguing that math is difficult... or about models, which may or may not contain all the needed data. models are a shortcoming of US, not the math! thanks.

How do you figure models must apply to the world but the mathematics used to construct and refine them must not? That makes no sense whatsoever

Of course it does. For example the mathematical topology predicts many shapes which we never observed in nature. On the other hand the mathematics doesn't allow model even the system of six gravitating bodies in deterministic way - such a system is too complex for it. Which is why the common people don't communicate the common world in math. If the math would be really such an effective way, we all would write just the math formulas here.

Ok First- just because we don't see examples of some mathematical predictions here doesn't mean they don't exist. Second- people use math all the time in common speech. Have you never been to the grocery store?

And I don't get this appeal to "intuition". Aren't any of you familiar with Daniel Dennet's multiple drafts theory? The brain is nothing more than a bunch of parallel processors feeding into a serial processor that acts sort of like a master control program we call consciousness. That's why you can be driving down the road and suddenly remember a name you couldn't before. Your brain kept crunching numbers until it found it then forwarded it to your conscious "mind". It's what psychologists used to call the AHA! experience. The brain is doing the same thing when it has these seemingly brilliant flashes of insight or enlightenment. There is no such thing as "intuition"

I don't get this article. Even if Platonism is wrong, and we can only make approximate models(btw: Quantum mechanics/Quantum field theory makes super freaking exact models) of reality, then why shouldn't we make "approximate" models of the whole reality/universe/multiverse ect. ? None-platonism seems to be bullshit out of the box because no one could really say if it's nature itself or just human imagination, would be no different. The whole point is, if we "ask" mathematical questions, then we get mathematical answer back from the universe, you can't deny this.

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